While each of the four steps can be problematic,
the optimization step is arguably the most conceptually and computationally difficult.
In particular, finding a solution for the desired Procrustes problem can be challenging. Moreover, any solutions are quite peculiar to the matrix manifold under consideration: the
symmetric Procrustes problem is largely unconnected to, say, the tridiagonal Procrustes problem.
Thus, in this article, we present many new solutions for (REF ) with different physics-informed matrix manifold constraints.
When exact solutions are not possible (e.g., if the manifold constraint is quite complicated)
there are sophisticated algorithmic solutions available [1]}.
